作　　者： ; ;

机构地区： 广东工业大学应用数学学院

出　　处： 《黑龙江大学自然科学学报》 2010年第5期625-629,共5页

摘　　要： 将θ-方法用于求解一类自变量分段连续型延迟微分方程,研究数值解的振动性以及数值方法对方程本身振动性的保持性质。通过对差分方程的分析,得到数值解在一般节点与整数节点处振动与非振动的等价性,进而获得了θ-方法的振动性条件,证明解析解的振动性能够被θ-方法保持。最后讨论了稳定性与振动性之间的关系。 Applying θ-methods to a class of the differential equations with piecewise constant arguments,the oscillation and the preservation of oscillation of numerical solution are studied.The equivalence of the oscillation and non-oscillation between the integer nodes and the any nodes are obtained by analyzing the difference equation.Furthermore,the conditions of oscillation for the θ-methods are given.It is proven that the oscillation of analytic solution can be preserved by the θ-methods.Finally,the relationship between stability and oscillation are discussed.

关 键 词： 数值解 方法 振动性

领　　域： [理学] [理学]